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\author{王立庆（2021级数学与应用数学1班） }
%\author{2022级数学与应用数学、应用统计学专业 }
\title{随机分析入门教学大纲（学生使用）}
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%\date{2022 年 12 月 15 日}

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\section*{时间地点}
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\item 上课时间地点：周二下午5-8节、周四下午9-12节，实验中心705. 
\item 答疑时间地点：周三上午8:30 - 11:30. 

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\section*{主要内容}
\begin{enumerate}
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\item  掌握布朗运动和条件期望的概念和计算。
\item  了解随机过程和鞅的概念。
\item  理解二次变差和伊藤积分的概念和计算。
\item  初步掌握伊藤引理的使用。
\item  模拟几何布朗运动的样本路径。
\item  理解随机微分方程的含义。
\item  求解随机微分方程的几个例子。
\item  了解金融数学的一些基本术语。
\item  理解Vasicek利率模型。
\item  理解BS期权模型和期权定价公式。

\end{enumerate}

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\section*{课程成绩}
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\item  平时成绩 100 \%.
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\item[1.1.] 课堂考勤4次，共30分。
\item[1.2.] 课堂练习3次，共30分。
\item[1.3.] 课外作业2次，共30分。
\item[1.4.] 阶段测验1次，共10分。
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%\item  期末成绩 60 \%.

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\section*{日程安排}

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\begin{tabular}{|M{1cm}|M{1cm}|M{3.5cm}|M{1.3cm}|M{6.5cm}|}  \hline 
周&星期&日期&章节&内容 \\ \hline 
17&二&2024年1月2日下午&1.1-1.5&随机过程、布朗运动、条件期望、鞅。		\\ \hline
17&四&2024年1月4日下午&2.1-2.4&伊藤积分、伊藤引理、几何布朗运动。		\\ \hline
18&二&2024年1月9日下午&3.1-3.4&随机微分方程、均值回复过程、数值解。		\\ \hline
18&四&2024年1月11日下午&4.1-4.2&Vasicek利率模型、BS模型。		\\ \hline
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\section*{参考文献}
\begin{enumerate}
\item  Thomas Mikosch著，王颖喆译，金融观点下的随机分析基础，北京师范大学出版社，2014年4月第1版。
\item  M. A. Pinsky, S. Karlin, An Introduction to Stochastic Modeling, Fourth Edition, 机械工业出版社，2013年2月影印版。
\item  张波，商豪，邓军，应用随机过程，中国人民大学出版社，2020年1月第5版。
\item  王军，邵吉光，王娟，随机过程及其在金融领域中的应用，清华大学出版社，2018年8月第2版。

\end{enumerate}

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